### Abstract

We compute the phase diagram in the N→∞ limit for lattice RP^{N-1}, CP^{N-1} and QP^{N-1} σ-models with the quartic action, and more generally for mixed isovector/isotensor models. We show that the N=∞ limit exhibits phase transitions that are forbidden for any finite N. We clarify the origin of these pathologies by examining the exact solution of the one-dimensional model: we find that there are complex zeros of the partition function that tend to the real axis as N→∞. We conjecture the correct phase diagram for finite N as a function of the spatial dimension d. Along the way, we prove some new correlation inequalities for a class of N-component σ-models, and we obtain some new results concerning the complex zeros of confluent hypergeometric functions.

Original language | English (US) |
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Pages (from-to) | 425-502 |

Number of pages | 78 |

Journal | Nuclear Physics B |

Volume | 601 |

Issue number | 3 |

DOIs | |

State | Published - May 14 2001 |

### Keywords

- Mixed isovector/isotensor model
- Nematic liquid crystal* N→∞ limit* 1/N expansion
- Nonlinear σ -model
- RP model* CP model* QP model* N -vector model

### ASJC Scopus subject areas

- Nuclear and High Energy Physics

## Fingerprint Dive into the research topics of 'Pathologies of the large- N limit for RP<sup>N-1</sup> , CP<sup>N-1</sup> , QP<sup>N-1</sup> and mixed isovector/isotensor σ -models'. Together they form a unique fingerprint.

## Cite this

^{N-1}, CP

^{N-1}, QP

^{N-1}and mixed isovector/isotensor σ -models.

*Nuclear Physics B*,

*601*(3), 425-502. https://doi.org/10.1016/S0550-3213(01)00065-7